Transition of deformation modes from bending to auxetic compression in origami-based metamaterials for head protection from impact

For the protection of the human head by energy absorption structures, a soft mechanical response upon contact with the head is required to mitigate the effect of impact, while a hard mechanical response for highly efficient energy absorption is required to stop the movement of the head. This study realized the opposite mechanical properties during head protection by transitioning the deformation mode from bending to auxetic compression. First, non-linear finite element (FE) models were constructed to numerically reproduce the bending behavior. The calculated force responses agreed well with forces in bending tests. Using the FE models, the EA structures with proper transition of deformation modes were designed and installed in the seat headrests of real vehicles. Head protection was evaluated by dynamic loading in sled testing, in which the force on the head of the crash test dummy was measured. The head injury criterion improved from 274 to 155, indicating the superior performance of the tested structures compared to that achieved by energy absorption structures based on steel plates. Moreover, the deformation of auxetic structures prevented neck bending by holding the head. These findings present new possibilities for effectively protecting the human body by mitigating impact, facilitating energy absorption, and ensuring head stability.


Design
The TMP unit cell was created by pairing the upper and lower origami sheets, as shown in Fig. 2a. The geometry is defined by the lengths l, m, and d and the internal angle of the parallelogram α . The change in the TMP geometry is characterized by the folding angles β , γ and the internal angle of the parallelogram α 32 : To show the state of the TMP, the folding ratio related to β was defined as follows: The cross sections of TMP tubes changed from convex shapes (for example, R = 25 % in Fig. 2b) to concave shapes (e.g. R = 50 % in Fig. 2b) as the folding ratio increased, where TMPs were created by pairing upper and lower origami sheets with l : m : d = 1 : 1 : 1 , α = 65 • . Because of the cross-sectional change, re-entrant shapes occur in TMP, which leads to auxeticity. The auxetic structures were designed and fabricated based on TMPs. As an example of auxetic structures with highly efficient EA, the geometrical parameters l = m = d = 12.5 mm , α = 65 • and R = 47.8 [%] were employed by scaling the TMPs used in a previous study 37 . These parameters provide auxeticity caused by the re-entrant shapes in the TMP. To install the auxetic structures in the headrest used in commercial vehicles, the tessellation of 8 × 2 × 2-unit cells shown in Fig. 2c provides an auxetic structure with dimensions of 146.3 mm (x) × 81.9 mm (y) × 55.1 mm (z) , which readily fits in real vehicle headrests. The number of tessellations were determined by confirming that the auxetic behavior is maintained during compression.

Manufacturing
The designed TMPs were fabricated as shown in Fig. 3. A fused filament fabrication (FFF)-type 3D printer (Flashforge, Adventurer3X) and commercially available nylon filament with a diameter of 1.75 mm (Markforged, Nylon White) were used to fabricate the auxetic structures. The test pieces were stored in water at 50 • C for 20 (1) tan(γ ) = tan(α) cos(β). www.nature.com/scientificreports/ h before the experiments to ensure that the nylon was in a water-absorbed state. This procedure was adopted because water absorption causes the nylon state to transition from glassy to rubbery.

Experimental setup/test
Quasi-static testing. To experimentally verify the deformation mode transition, the force response of auxetic samples sandwiched between upper and lower plates was measured through quasi-static bending tests, as shown in Fig. 4. The sandwich structures were constrained at the left and right boundaries of the lower plates. The upper and lower panels were 1-mm-thick nylon and aluminum (A5052), respectively. The auxetic structures were compressed by moving a cube whose diameter was 165 mm downwards. A standard compression-testing machine (Instron 5566) was used to perform quasi-static bending tests. The maximum deformation was 50 mm, and the compression speed was set to 5 mm/min to prevent inertial effects. The compression of the test pieces was recorded using a digital video camera (Panasonic HC-W870M).

Dynamic testing.
To imitate the dynamic load caused by the acceleration experienced during a vehicle crash, a commercial sled test system driven by compressed air was used, as shown in Fig. 5a. The sled testing was conducted using 1.2-mm-thick auxetic structures. The lower panels were made of two 1-mm-thick aluminum plates layered together and connected to the seat frame using bolts. In addition, the top of the auxetic structures was covered with a 1-mm-thick nylon plate, as shown in Fig. 5b. A commercial 1.4-mm-thick cold steel plate (JIS G 3141) with trapezoidal shapes (upper dimension of 160 mm, lower dimension of 200 mm, and height of 75 mm) was also used in the sled testing, as shown in Fig. 5c, to contrast the performance of the auxetic plates against common EA structures.
The acceleration was generated based on the UN-80 regulation 63 using compressed air to move the commercial sled test system (HyperG 220, Dr. Steffan Datentechnik). The forces on the head, chest, and neck of the dummy set on the right seat (front side of Fig. 5a) were measured during the test, and the movement of the head was recorded via the sled test system. The HIC was calculated as 64 : www.nature.com/scientificreports/ where a is acceleration at head of dummy, t 1 and t 2 are two time points such that 0 < t 1 < t 2 < T , and T is the duration of the impact.

Finite element analysis (FEA)
To numerically reproduce the deformation process during the bending experiments, nonlinear finite element analysis (FEA) was performed using a commercial software (LS-DYNA 65 ), as shown in Fig. 6. A quasi-static simulation was performed using an explicit dynamic scheme to consider the contact between the auxetic panels under a stable state. The auxetic structures were constrained at both the left and right edges of the lower plates of the sandwich structures. The auxetic structures were deformed by the downward displacement of a rigid cube. Four-node shell elements were used to model the panels. Furthermore, the materials were assigned elastoplastic constitutive laws based on the stress-strain curves of the auxetic cores and upper panels, which were obtained www.nature.com/scientificreports/ from three-point bending tests performed on rectangular plates additively manufactured with the same materials used in the fabrication of the auxetic structures. The Young's modulus obtained from the three-point bending test was 332 MPa. The mass density and Poisson's ratio were 1162 kg/m 3 and 0.4, respectively, as shown in Table 1.
In addition, the lower plates were modeled using the stress-strain curve of A5052 66 , with Young's modulus, density, and Poisson's ratio of 70 GPa, 2910 kg/m 3 , and 0.33, respectively 67 . The thickness of the shell elements adjacent to the crease of the origami was increased by 1 mm. The friction between the panels was set as 0.2, and that between the panels and the rigid cube was set to 0.5. Figure 7a shows the force-displacement curves during compression of the auxetic structures sandwiched with panels by rigid cubes through experiment and FEA. The tests were performed for auxetic structures with 1.0-, 1.2-, and 1.4-mm-thick panels. The force responses increased linearly with the displacement of the rigid cube until approximately 20-mm deformation, where global bending is dominant (i.e., the re-entrant shapes of TMPs in zy-plane do not shrink in FEA.) as shown in Fig. 7b. However, the force responses plateaued after the deformation mode transitioned to auxetic compression (i.e., the re-entrant shapes of TMPs shrank in FEA under 30-and 40-mm deformation). Therefore, the proposed structures exhibit soft mechanical properties under small deformations and hard mechanical properties under large deformations. The transition of mechanical properties is suitable for the realization of both impact mitigation after impact and high EA to prevent head movement. In addition, the plateau force owing to auxetic compression changed with the thickness of the plates consisting of auxetic structures, which enabled us to easily adjust the EA. Furthermore, the effects of mesh sizes were investigated by changing the number of splits in the side of parallelogram from 3 to 10 as shown in Fig. 8. Although force responses obtained from FE model discretized  www.nature.com/scientificreports/ with mesh by three splits were unstable, other force responses were approximately stable among the FE models discretized by different mesh sizes. In this study, the FE models were discretized with mesh sizes with six splits, which is sufficient to obtain stable force responses.

Results and discussion
Investigation of design parameters. To design the bending deformation of the EA structures, the effects of the thickness of constrained plates were investigated by changing the thickness of the constrained panels from 0.5 mm to 1.5 mm in FEA used in Fig. 7. As shown in Fig. 9, the larger thickness of constrained panels increases the slope between displacement and force, which transits deformation modes from bending to auxetic compression in small displacements. In contrast to the difference in global bending, the thickness of constrained panels has no significant influence on the plateaued force. Therefore, we can independently design soft responses for impact mitigation by considering the thickness of the constrained plate. Furthermore, the numbers of stacked layers were investigated by changing the number of tessellation of the TMPs in the z-direction based on the FEA models used in Fig. 7. As shown in Fig. 10a, the force response of the 1-layered TMP plateaued at approximately 20-mm displacement. However, the lack of TMP cells disrupted the auxetic behavior (i.e., the cross-section in zy-plane expands during deformation) as shown in Fig. 10b, which caused a dip of force responses in approximately 30-mm displacement and increased the force by densification for  www.nature.com/scientificreports/ displacements larger than 40 mm. In contrast, as the auxetic behavior of the 2-layered TMP was not broken (i.e., the cross-section in zy-plane shrinks during deformation), the plateaued force response continued in the long displacement region. Moreover, the forces of 3-layered TMPs were more ideally plateaued. These results suggest that a larger number of layers in TMP provide plateaued forces in the long displacement region. In contrast to the plateaued phase, the global bending in the early stage of displacement was not influenced by the number of layers because TMPs flexibly deform in x-axis direction by their one-degree-of-freedom motions. Therefore, we can choose the number of layers to satisfy the required EA under geometric limitations. In this study, the 2-layer TMPs were installed in the headrests as the minimum number of layers for obtaining the long plateaued force. www.nature.com/scientificreports/ Energy absorption under dynamic loading. Figure. 11 shows the comparison of force responses on the head from steel plate and auxetic structures. Because the steel plate causes a dip in the force response after contact with the head (20-mm displacement), the lack of EA generates force peaks in the later stage of deformation by the contact of the head with the seat frame (75-mm displacement). In contrast, the auxetic structures generate a plateau force response (from 20 to 40-mm displacement) after contact with the head without increasing the initial peak of the force responses compared to the steel plates, which provides a highly efficient EA, as confirmed in the quasi-static testing shown in Fig. 7. Owing to the difference in EA, the contact between the head and seat frame that occurred around a 75-mm displacement in the steel plate was prevented by the auxetic structure; consequently, the maximum force on the head reduced from 3 to 2.5 kN. Furthermore, the HIC associated with the likelihood of head injury significantly improved from 274 to 155. Therefore, the proposed concept provides efficient head protection. Although the auxetic structures were designed via quasi-static loading, the low initial peaks and plateaued force responses were maintained in the dynamic loading by sled testing. Therefore, the proposed structures effectively mitigated high-velocity impacts, such as those encountered in vehicle crashes. Furthermore, the motions of the crash test dummy were compared between sled tests using a steel plate and the auxetic structures, as shown in Fig. 12a. The neck of the dummy bent during the deformation of the steel plate, resulting in contact between the chest and seat, as shown in Fig. 12a. However, the neck of the dummy does not bend after contact with the auxetic structure, which prevents contact between the chest and seat. The difference in motion is evidenced by the moment of the neck and the shear force of the chest, as shown in Fig. 12b. The prevention of neck bending relies on the unique curvature caused by the bending of the auxetic structures. Although conventional plates (i.e., those with a positive Poisson ratio) generate negative-Gaussian curvatures (i.e., hyperbolic surfaces), it is known that the bending of auxetic structures generates positive-Gaussian curvatures (i.e., bowl-shaped). The bowl curvature can easily fit the shape of the head. In contrast, because the bending of a conventional steel plate does not generate a curvature fitting to the head, the head of the dummy appears to slip upward after contact. Therefore, the bending of auxetic structures could have the potential to improve head protection by deformation, allowing easy fitting around the head.

Conclusion
This study demonstrated head protection in a vehicle crash situation based on the transition of the deformation mode from bending to auxetic compression, which provides soft mechanical responses for impact mitigation after contact with the head and hard mechanical responses for high-efficiency EA during the deformation of auxetic structures. First, the transition of the deformation mode was modeled by FE analysis, and the models were verified by experimental quasi-static bending tests. Following the deformation mode, their force responses also shifted from soft to hard and plateaued. Furthermore, the auxetic structures were equipped on the headrests of seats in real vehicles, and head protection was evaluated by sled testing. The force on the head of the crash test dummy from the headrest was evaluated under artificial acceleration conditions imitating a vehicle crash. In the sled testing, the maximum force at the head reduced from 3 to 2.5 kN, and the HIC significantly improved from 274 to 155 compared to the case of common steel-plate EA structures. Furthermore, the deformation of auxetic structures prevented the bending of the neck by holding the head. Therefore, the transition of deformation modes in auxetic structures is beneficial for the efficient protection of the human body via the realization of impact mitigation, EA, and head holding.
In this study, the condition of dynamic loading was limited to head collision under vehicle crash situations. To extend the application of the proposed structures to various types of crash scenarios, it is important to investigate the effect of strain rate in wider applications. Furthermore, it is important to explore the bending behavior  Figure 11. Force at the head of the dummy during the sled test. After the contact between the head and EA structures, the head is subjected to a force of approximately 2.0-2.5 kN and the auxetic structures provide high EA due to their plateau force response, preventing the head from making contact with the seat frame.

Data availability
The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.  www.nature.com/scientificreports/